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Thursday, October 20, 2016

Estimation of missing tip states under Brownian motion using likelihood

As I have noted
previously,
it is possible (and relatively straightforward) to reconstruct missing tip
values under Brownian motion by jointly maximizing the likelihood of internal
and (missing) terminal states using likelihood.

This is implemented in the phytools function anc.ML.

One attribute of these reconstructed values is that they will precisely match
the reconstructed ancestral node state of their immediate parent. This is
totally unsurprising because under Brownian motion because the expected
change over any time period is zero (with variance equal to the product of
the Brownian rate, σ2, and the edge length).

We can visualize this phenomenon using both phenogram and
contMap. Here's what I mean.

Recently, it was reported to me that for some empirical dataset this has not
been observed to be the case. The most likely explanation for this is non-
convergence of the ML optimization by anc.ML. This can be
ameliorated by increasing maxit, but this may not guarantee
convergence on relatively large trees. I'm sure that a better solution
exists, unfortunately I have not worked on this in a bit.

About this blog

This web-log chronicles the development of new tools for phylogenetic analyses in the phytools R package. Unless you a reading a very recent page of the blog, I recommend that you install the latest CRAN version of phytools (or latest beta release) before attempting to replicate any of the analyses of this site. That is because the linked functions may be archived, and very likely have been replaced by newer versions.